The modified Euler equation for the correlation function in the case of a many-fermion system and study of its asymptotic behaviour

Abstract

In a recent pape r (1), the p rob lem of the de te rmina t ion of the J a s t row corre la t ion func t ion ](r) was discussed and some modif ied in tegro-di f ferent ia l Euler equa t ions were ob ta ined for this h m c t i o n in t he case of impure nuclear m a t t e r and a many-pa r t i c l e boson system. The case of a manyfe rmion system, l ike nuc lear ma t t e r , had not been t r ea ted in detai l . I t is the purpose of th is paper to give and to s t udy the cor responding modif ied Eu le r equa t ion for such a sys tem, which arouses also pa r t i cu la r in te res t because of t he possibi l i ty of obta ining, under cer ta in condi t ions, an app rox ima te a sympto t i c fo rm of the solution. The func t iona l of the energy per pa r t i c l e for a manyfe rmion system, in the f o r m given by AWLES (2), is considered: 22 ) ] (1) N 5 2~ § 2Jl\Fm [(v/)2-/v2]]§ V(r)/2 GF(r)--2~-2V/2F(r) dr ,